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Integral of x/sqrt((x+1)^2-4) dx

Limits of integration:

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The solution

You have entered [src]
  1                     
  /                     
 |                      
 |          x           
 |  ----------------- dx
 |     ______________   
 |    /        2        
 |  \/  (x + 1)  - 4    
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \frac{x}{\sqrt{\left(x + 1\right)^{2} - 4}}\, dx$$
Integral(x/sqrt((x + 1)^2 - 4), (x, 0, 1))
The answer (Indefinite) [src]
  /                             /                       
 |                             |                        
 |         x                   |          x             
 | ----------------- dx = C +  | -------------------- dx
 |    ______________           |   __________________   
 |   /        2                | \/ (-1 + x)*(3 + x)    
 | \/  (x + 1)  - 4            |                        
 |                            /                         
/                                                       
$$\int \frac{x}{\sqrt{\left(x + 1\right)^{2} - 4}}\, dx = C + \int \frac{x}{\sqrt{\left(x - 1\right) \left(x + 3\right)}}\, dx$$
The answer [src]
  1                        
  /                        
 |                         
 |           x             
 |  -------------------- dx
 |    ________   _______   
 |  \/ -1 + x *\/ 3 + x    
 |                         
/                          
0                          
$$\int\limits_{0}^{1} \frac{x}{\sqrt{x - 1} \sqrt{x + 3}}\, dx$$
=
=
  1                        
  /                        
 |                         
 |           x             
 |  -------------------- dx
 |    ________   _______   
 |  \/ -1 + x *\/ 3 + x    
 |                         
/                          
0                          
$$\int\limits_{0}^{1} \frac{x}{\sqrt{x - 1} \sqrt{x + 3}}\, dx$$
Integral(x/(sqrt(-1 + x)*sqrt(3 + x)), (x, 0, 1))
Numerical answer [src]
(0.0 - 0.684853256107041j)
(0.0 - 0.684853256107041j)

    Use the examples entering the upper and lower limits of integration.